Branched Polymers and Gels

Abstract

Polymers are giant molecules that are made of millions of atoms. They are the repetition of an elementary unit called monomer. They are used as plastics, paints, adhesives, rubbers, and in some future, as batteries. They have changed completely our everyday life by superseding natural materials such as wood, iron, etc. Our understanding of the structure of synthetic polymers has increased tremendously these last 20 years. They may be either linear or branched. In the former case, one makes react divalent monomers, that may interact only by two functional units, leading to a linear structure. In the latter case, multifunctional units react, leading to a structure that is randomly branched. A very interesting aspect of this type of reaction is that as time proceeds, one eventually goes from a viscous fluid called a sol to an elastic solid called a gel. The sol-gel transition was considered first in the forties in its mean field version by Flory and by Stockmayer and Zimm. It was improved recently by noting that it is directly related to the percolation transition in Physics (de Gennes, 1976; Stauffer, 1976). More recently, the fractal aspects of these branched polymers and gels were considered both theoretically and experimentally. Although the ideas developed for these synthetic polymers are probably too simplistic for direct use in biological problems, we believe that some of them might survive even when complications such as rigidity, presence of electrical charges, and eventually others are taken into account. In what follows, we will discuss the simplest possible case of sol-gel transition.